Joint facies and rock properties Bayesian amplitude‐versus‐offset inversion using Markov random fields

Abstract

ABSTRACTSeismic reflection pre‐stack angle gathers can be simultaneously inverted within a joint facies and elastic inversion framework using a hierarchical Bayesian model of elastic properties and categorical classes of rock and fluid properties. The Bayesian prior implicitly supplies low frequency information via a set of multivariate compaction trends for each rock and fluid type, combined with a Markov random field model of lithotypes, which carries abundance and continuity preferences. For the likelihood, we use a simultaneous, multi‐angle, convolutional model, which quantifies the data misfit probability using wavelets and noise levels inferred from well ties. Under Gaussian likelihood and facies‐conditional prior models, the posterior has simple analytic form, and the maximum a‐posteriori inversion problem boils down to a joint categorical/continuous non‐convex optimisation problem. To solve this, a set of alternative, increasingly comprehensive optimisation strategies is described: (i) an expectation–maximisation algorithm using belief propagation, (ii) a globalisation of method (i) using homotopy, and (iii) a discrete space approach using simulated annealing. We find that good‐quality inversion results depend on both sensible, elastically separable facies definitions, modest resolution ambitions, reasonably firm abundance and continuity parameters in the Markov random field, and suitable choice of algorithm. We suggest usually two to three, perhaps four, unknown facies per sample, and usage of the more expensive methods (homotopy or annealing) when the rock types are not strongly distinguished in acoustic impedance. Demonstrations of the technique on pre‐stack depth‐migrated field data from the Exmouth basin show promising agreements with lithological well data, including prediction accuracy improvements of 24% in and twofold in density, in comparison to a standard simultaneous inversion. Much clearer and extensive recovery of the thin Pyxis gas field was evident using stronger coupling in the Markov random field model and use of the homotopy or annealing algorithms.